Continuity mistake: When Krennic is first talking with Galen Erso on his home planet, the coat that Galen is wearing is visibly drenched, presumably from rain water, but later in the scene, when Lyra Erso intervenes, the dampness on his coat is now much lighter. (00:03:30 - 00:05:10)
Suggested correction: We know from Episode IV that some fabrics in the Star Wars canon dry very quickly, see the garbage compactor aftermath. This is totally possible.
I'm not sure if this is a viable explanation. While some aspects of life in the Star Wars universe are somewhat fantastical (the ways of the Jedi for example), this universe still follows the same basic psychics of Earth, so for example, something like gravity or the speed at which something dries would still be the same. (As for your Episode IV reference, I'm not sure if that counts as a defence, or is just a mistake in of itself).
Continuity mistake: When Director Krennic and Governor Tarkin are discussing testing the Death Star, Krennic says he will not fail and turns around to leave. As he turns, an Imperial officer is seen standing a couple of meters away from him in the background, but in the next shot, the Imperial officer is suddenly right behind him. (00:23:20)
Suggested correction: That is not correct, Captain Dunstig Pterro is not that far, and Krennic moves pass him and then Pterro follows.
